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# In a Regular Pentagon Abcde, Inscribed in a Circle; Find Ratio Between Angle Eda and Angle Adc. - ICSE Class 10 - Mathematics

ConceptArc and Chord Properties - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle

#### Question

In a regular pentagon ABCDE, Inscribed in a circle; find ratio between angle EDA and angle ADC.

#### Solution

Arc AE subtends ∠AOE at the centre and
∠ADE at the remaining part of the circle.

∴ ∠ADE  = 1/2 xx 72°
= 36                   [central angle is a regular pentagon at O]